Posted at 12.17.2018
Water hammer result is normally taking place inside our life and only that people not realize it. A typical example of a drinking water hammer occurs generally in most homes every day: Simply turning off a bathtub quickly will send a loud thud through the home. This paper check out the parameters that triggers water hammer effect. Parameter that could have an effect on would be region of pipe, material of pipe, pressure in tube and length of pipe. Test would be conduct to research the guidelines that have an impact on the normal water hammer effect. These discrepancies are based on the essential assumptions found in the derivation of this particular hammer equations for the liquid unsteady pipe flow. The newspaper presents an examination of this hammer experimental test performed by the LMS DAQ system. The LMS would be research by FFT sign and by FFT final result convert to wave speed. Such information can be used further for a far more detailed system review and development of improvements or preventive activities.
Pressure surge or drinking water hammer, as it is commonly known, is the formation of pressure waves as the consequence of a sudden change in liquid speed in a piping system. Water hammer usually occurs when a fluid flow starts or halts quickly or is compelled to produce a rapid change in path. Quick closing of valves and stoppage of any pump can create normal water hammer [14, 7, 9, 10, 11, 12, 13, 14, 21]. A valve shutting in 1. 5 s or less depending upon the valve size and system conditions causes an abrupt stoppage of the movement. Since water is not compressible, any energy that is put on it is instantly sent. The pressure waves (acoustic influx) created at immediate valve closure can reach five times the system's working pressure. Thus, investigations of water hammer result can be carry out by an test.
The earliest software of the one-dimensional wave equation to clarify observed drinking water hammer results was created by Joukowsky in 1898 [8, 9, 10]. Joukowsky appropriately predicted the utmost line pressures and disruption propagation times in a normal water distribution system where rapid valve closures took place. Joukowsky's formula is expressed as
where ОP is the pressure go up due to the normal water hammer in N/m2, a is the speed of impulse waves in m/s, ОV is the velocity change of liquid in the pipeline in m/s, and П is the density of the liquid in kg/m3. The aforementioned relation may also be written as
where ОH is the pressure increase due to the drinking water hammer in terms of column of water in meters and g is the gravitational acceleration in m/s2. In deriving the aforementioned equations the next assumptions were made:
The friction losses are much smaller than the static pressure in the tube.
Flow is sole stage and there are no dissolved gases in the water.
The liquid speed change occurs in a time significantly less than the critical time.
The fast stop LMS algorithm uses the fast Fourier transform (FFT) to transform the input indication x(n) to the consistency domains. This algorithm also updates the filtration coefficients in the frequency area. The FFT signal can be transform and replacement to equation
The first to successfully investigate this particular hammer problem was the Italian engineer Lorenzo Allievi which Normal water hammer can be examined by two different approaches, rigid column theory which ignores compressibility of the substance and elasticity of the surfaces of the tube, or by a full analysis including elasticity .
The earliest software of the one-dimensional wave equation to describe observed water hammer effects was created by Joukowsky in 1898 [8, 9, 10]. Joukowsky properly predicted the utmost line pressures and disturbance propagation times in a normal water distribution system in which abrupt valve closures took place. Joukowsky's equation is portrayed as
where ОP is the pressure surge due to the water hammer in N/m2, a is the speed of impulse waves in m/s, ОV is the speed change of liquid in the pipeline in m/s, and П is the density of the water in kg/m3. The above mentioned relation can even be written as
where ОH is the pressure increase due to the normal water hammer in terms of column of drinking water in meters and g is the gravitational acceleration in m/s2. In deriving the above equations the following assumptions were made:
The friction loss are much smaller than the static pressure in the pipe.
Flow is one phase and there are no dissolved gases in the water.
The liquid velocity change occurs in a period significantly less than the critical time. Critical time can be acquired from
Where tr is the critical time which is thought as the time in which the pressure waves would reflect and L is the distance between your point at which the pressure waves are made and the nearest point of which they would indicate.
The swiftness of the pressure waves, a, is a function of the next parameters:
1. Specific weight and elasticity component of the liquid.
2. Tube diameter, wall width, and the length between the support details.
3. The elasticity component of the tube material.
The derived relationship for calculating the pressure influx speed is really as follows:
Where D is the tube diameter, e is the tube wall thickness, E is the elasticity module of the pipe material, K is the elasticity component of the liquid, and C1 is a continuous that may be assumed to be add up to one.
Pressure waves in pipelines are made due to different normal businesses in the machine such as beginning and closing the valves, set up or shutting down the pumps, or any rapid change in the pump rotational swiftness [10, 12].
Generally, the sources that may have an impact on the normal water hammer attenuation, shape and timing is the pressure in tube, velocity movement in tube, and rapid change of speed flow. However there may be other sources that may have an effect on the waveform predicted by classical normal water hammer theory include viscoelastic behavior of the pipe-wall materials, blockage and leakage in addition to the previously reviewed unsteady friction, cavitations and fluid-structure discussion. These discrepancies derive from the derivation of water hammer equations for the liquid unsteady tube circulation .
There are several solutions to analysis the water hammer impact such as FAST method, numerical modal method, validation, wave method, characteristic method, and etc.
Fourier amplitude level of sensitivity test (FAST) method is the sensitivity study which seeks to determine the most crucial input variables that are major contributors to the model outcome uncertainty.
In this work, as an illustration, RELAP5 research of a normal water hammer test was performed.
The tests were conducted using the energetic behavior of shutting and beginning valves in a steady-state water movement. A centrifugal pump produces steady-state movement into the circuit from the pressurized vessel into the test pipe section . Through the first phase of the transient, a rarefaction wave is going inside the pipe for the downstream reservoir. As a result, cavitation occurs downstream the valve, and a vapour bubble is shaped. The made pressure wave oscillates between the vessel and the vapour bubble before cavitation condenses, inducing a cavitational hammer.
Figure 3. 1 - Comparison of the RELAP5 basic case calculation with UMSICHT experimental data
After that, they choose and qualify the most important parameters for the sensitivity analysis for FAST method. The first-order sensitivity index is computed and the bigger order sensitivity indices calculate the contribution of the interactions of various input parameters into the model end result variance. After that, total up the whole level of sensitivity index and total impact sensitivity index reveals the amount of interaction between the parameter appealing and the rest of the parameters. This index provides important more information and may be used to determine strong discussion effects among the input parameters or even to prove absence of the relationships.
The approach to characteristics (MOC) is conceptually slightly sophisticated and requires numerous steps or calculations to solve an average transient pipe circulation problem. As the complexity of the tube system increases, the amount of required calculations boosts and for useful applications your computer program is necessary. Various computer programs have been developed predicated on the MOC and types of procedures for handling tube junctions, pumps, surge tanks, and cavitations have been included are almost all of these programs [3, 4, 11].
This method is dependant on the physically accurate idea that the transient tube stream results from the technology and propagation of pressure waves that arise consequently of a disruption in the tube system ~valve closure, pump trip, etc. !. A pressure influx, which represents a rapid pressure and associated move change, journeys at sonic speed for the liquid-pipe medium, and the wave is partially sent and reflected whatsoever discontinuities in the pipe system ~tube junctions, pumps, wide open or closed down ends, surge tanks, etc!. A pressure wave can be modified by tube wall amount of resistance. This explanation is the one which closely symbolizes the actual system of transient tube flow. Within this paper this method is known as the wave quality method (WCM) [3, 4, 19].
Figure 3. 2 - Assessment of results of wave characteristic and approach to characteristics contrast.
Transient (drinking water hammer) analysis is vital to good design and operation of piping systems. This important evaluation can be done using the mathematically based mostly MOC or the WCM predicated on the action of pressure waves. The MOC and WCM methods are both capable of accurately handling for transient stresses and moves in water distribution networks like the effects of tube friction. The MOC requires calculations at interior tips to handle the influx propagation and the effects of tube friction. The WCM handles these effects using pressure waves [3, 19].
An experiment is established as physique below .
Figure 3. 3 - Experiment set up
The experiment is performed with the initially open with a fully developed movement; the valve was then closed down for the rest of the trial. If the valve is sealed a good pressure influx propagates from the valve. This influx bounces between your tank and the valve until the pressure everywhere in the tube is add up to the pressure in the reservoir . The result would be mainly like the Flownet simulation final result graph .
The result of pressure sensor and make sensor is accumulated and the graph is plotted as shape below:
Figure 3. 4 - Pressure and push plots for valve final .
Mathematical model and numerical solution is the method whereby using the numerical solution solution to compute the theoretical evaluation of normal water hammer in tube. The calculations of pipe as shown equations below and until it get the answer of H(t) meter [2, 5, 8, 9, 18].
By using numerical solution, a first order finite difference method is applied. If the Courant quantity (aDt/ Ds) is 1, this technique is exact. Normally, interpolation along time or space is necessary. After the calculation, the Head meter (by calculation) is story. All computations have been performed always supposing a Courant number equal to 1 and a single time step Dt for your system .
Figure 3. 5 - Storyline H(t) with interpolation
To prevent the severe pressure surge during a water hammer occurrence, the next methods can be used [10, 12, 13 15]:
Design the Discharge Pipe Based on Lower Water Velocities.
- By lessening the flow speed, the effect of this hammer will be reduced.
Increasing the Moment of Inertia of the Pump.
- Adding a flywheel on the rotating axis of the traveling motor would prevent the rotational speed to reduce sharply and for that reason restrain the surplus pressure cut down or increase. This method is usually inexpensive for small pump channels and the release pipes for up to 3 km.
- Among the simpler solutions to prevent the harmful effects of this particular hammer is to install a by-pass tube with a non-return valve. Under normal conditions, the pressure supplied by the pump would keep carefully the non-return valve closed. However, following the shutdown of the pump, pressure will be decreased in the discharge pipe as soon as it becomes significantly less than the suction pressure, the non-return valve will open up and the liquid would get into from the suction pipe to the discharge pipe thereby stopping more pressure decrease. This method may be used in systems in which the supplied brain of the pump is not very high.
- These tanks become a tank to reduce the pressure waves and are installed on the release pipe. Once the pressure in the pipe increases, liquid gets into the tank and is also stored there. During times of subnormal pressure in the pipe, then, the liquid would flow back to the pipe, protecting against rapid speed changes .
- Air chambers are essentially a kind of ruthless surge tanks which can be built in smaller sizes. In these tanks, the pressurized air locates on the top of liquid. How big is the chamber must be large enough to compensate the liquid in the subnormal pressure periods without allowing air to enter the system. The volume of mid-air must be chosen such that during filling period of the pipes, its pressure does not change significantly.
- The release pipes of the pumps are usually equipped with non-return valves. The main application of these valves is to avoid the flow working toward the pump when it ceases, thereby minimizing the adverse effects. During normal working conditions of the pump, the resource flow would keep carefully the non-return valve available. Upon immediate stop of the pump, the movement rate would reduce swiftly until it reaches zero and would then flow back to the pump. Once the liquid circulation is reversed, the disk of the valve is sharply shut, causing an intense effect on the valve seating. This might create more pressure waves. Neglecting the pressure losses, this pressure go up is equivalent to the subnormal pressure produced when the stream returns back again to the pump.
Pressure Control Valves.
- These valves are designed to open at very high stresses and are installed at the critical details of the piping system. During the pressure surge period, the valve would release liquid to the exterior. This would decrease the pressure in the lines and inhibits any possible injuries.
- These valves are installed on those things of the piping system where there is a possibility of water evaporation anticipated to subnormal pressures. When the pressure reduces beyond certain level in the pipe, these valves close and allow atmospheric air to get into the system.
Fifure4. 1 - Flow graph of the Project
Figure above shown the circulation of the job, which the task begins from the Literature review and than the experiment set up. Following the experiment analysis is done, the prevention of water hammer is suggested. The experiment will be evaluation base on reduction method.
In this task, an test would be carry out to examination the parameter that affects this hammer effect.
Apparatus which include: ѕ' PVC tube, ѕ' steel pipe, 1' PVC tube, surge tank, pump with inverter, fitting, connector, pressure gauge, and LMS DAQ system.
Figure 4. 2 - Test set up
An experiment is set up as shape 1 to analysis the parameter that impacts this particular hammer result. The parameter examined would be the area of pipe, material of pipe and the distance of the pipe. The tube with difference parameter would be putting in at the tested area.
Sensor of the LMS would put at the tried area and data would be gather by DAQ system. The FFT indication would be taking and the transmission is determined in the wave acceleration. The graph would be story by the LMS DAQ system and by calculation of wave speed, the graph of wave velocity versus the consistency also would be plot.
The data of the FFT signal will be taken after the immediate shut down valve. The wave speed of tube will be computed as table 3. 1.
Table 4. 1 - Exemplory case of data collecting
The expected result of the graph form by LMS FFT sign would be shown as shape 3. 2 below .
Figure 4. 2 - Expected FFT altered transmission in pipe
After have the FFT transmission, the measured pressure signals were FFT altered and substituted to
to obtain consistency series wave rate data.
After have the frequency wave rate data, the graph of influx swiftness versus the regularity is ploted .
Figure 3. 3 - Expected wave speed graph
By the wave acceleration data, we can compare the wave swiftness by theoretical computation as below:
Where D is the pipe diameter, e is the tube wall thickness, E is the elasticity module of the tube material, K is the elasticity module of the liquid, and C1 is a frequent that can be assumed to be equal to one.
After the analysis of parameter that impacts this particular hammer, elimination or lowering of drinking water hammer method would be suggested. Another test will be do to prove the prevention of drinking water hammer can be used.
The Gantt graph that acquired planed as below:
Figure 5. 1 - Gantt graph of project planning
From the Gantt chart, the test should setup in at September. However, the experiment is setup in October. This is due to some delay of the item finding. The improvement report and the thesis is also start writing since Sept. Test will be start after the experiment done set up. If possible, the experiment may begin at sooner than planning.
As summation, the progress of the job is still in enough time planning routine.
The scientific study of normal water hammer fluid move has been carried out since the midsection of the nineteenth century. As will additionally apply to every other portion of engineering research, a great many advances have been made in the exactness of analysis and the range of applications since that time. Although just a few simple problems were approachable by previous analytical methods and numerical techniques, a much broader spectrum of drinking water hammer problems could be fixed once graphical methods were developed.
Although there are a lot of water hammer avoidance methods, the hammer seen still happen in our real life. Therefore, the experts or technical engineers today still keep hands on the task of analysis of normal water hammer result.
A drinking water hammer research should be an integral part during the design period for a new project, and if potential water hammer problems are recognized, then the best performing selection of security devices should be installed to the system.